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9.Question 9Consider two identical light clocks, designed as explained in lecture. Bob has one, and Alice takes the other on her spaceship and flies by Bob at speed V. Bob observes Alice’s clock. What is the relationship between the duration of one tick on Bob’s clock and the duration of one tick on Alice’s clock, according to Bob (where γ represents the Lorentz factor)? (Tip: Think about the light clock diagram and the value of the Lorentz factor.)1 pointThe duration of one tick on Alice’s clock = (1/γ) times the duration of one tick on Bob’s clock.The duration of one tick on Alice’s clock = the duration of one tick on Bob’s clock.The duration of one tick on Alice’s clock = γ times the duration of one tick on Bob’s clock.

Question

9.Question 9Consider two identical light clocks, designed as explained in lecture. Bob has one, and Alice takes the other on her spaceship and flies by Bob at speed V. Bob observes Alice’s clock. What is the relationship between the duration of one tick on Bob’s clock and the duration of one tick on Alice’s clock, according to Bob (where γ represents the Lorentz factor)? (Tip: Think about the light clock diagram and the value of the Lorentz factor.)1 pointThe duration of one tick on Alice’s clock = (1/γ) times the duration of one tick on Bob’s clock.The duration of one tick on Alice’s clock = the duration of one tick on Bob’s clock.The duration of one tick on Alice’s clock = γ times the duration of one tick on Bob’s clock.

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Solution

The duration of one tick on Alice’s clock = γ times the duration of one tick on Bob’s clock.

This is due to the time dilation effect in special relativity. When Alice is moving relative to Bob, Bob will observe Alice's clock to be ticking slower. The factor by which it is slower is given by the Lorentz factor γ.

Similar Questions

7.Question 7Consider two identical light clocks, designed as explained in lecture. Bob has one, and Alice takes the other on her spaceship and flies by Bob at speed V. Bob observes Alice’s clock as Alice flies by. Which of the following statements is true?1 pointBob observes Alice’s clock to tick faster than his clock.Bob observes Alice’s clock to tick at the same rate as his clock.Bob observes Alice’s clock to tick slower than his clock.

Question 3Consider the twin paradox example done in lecture: On Alice's outbound trip to the star, Bob observes Alice's clocks running slower than his clocks. What does Alice observe regarding Bob's clocks?

9.Question 9In the twin paradox example done in lecture, just after Alice leaves the star on her return trip (and she's back up to her cruising speed of 0.6c), she observes Bob's clock back where he is located. (In other words, she has a photo taken of his clock and her corresponding clock at that location, her clock being part of her lattice of clocks.) Compared to her clock, does she observe Bob's clock to be behind, ahead, or the same time as hers?1 pointBob's clock is behind her clock.Bob's clock is ahead of her clock.Bob's clock has the same time as her clock.

10.Question 10In the twin paradox example done in lecture, how does Alice explain the fact that when she returns, Bob has aged more than she has, even though on both legs of her trip when she was traveling at 0.6c she observed his clocks to run more slowly than hers?1 pointDue to the finite speed of light, there is a delay in when Alice sees the reading on one of Bob's clocks, which means that Alice's observation of Bob's clocks running slow is incorrect.When she turned around at the star, she changed her frame of reference, which led to his clocks jumping ahead of hers (from her perspective).Though it seemed to Alice as if Bob's clocks were running slower than hers, they were actually running faster throughout the whole trip.

2.Question 2Consider a situation that is similar to that in one of the video lectures, i.e., Alice observing Bob traveling from Earth to a star at a certain distance from Earth. Assume that the Lorentz factor for the relative velocity between Alice’s frame of reference (the Earth-star frame of reference) and Bob’s frame of reference (the spaceship frame of reference) has a value of 3. Alice, in her frame of reference, measures the distance to the star as 18 light years. What is the distance from Earth to the star in Bob’s frame of reference?1 point54 light years18 light years0 light years6 light years

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